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On Tuesday in New York, modern art collectors will get the chance to spend tens of millions dollars on paintings such as Gerhard Richter’s “Abstraktes Bild (712)”, which is on sale with an estimated value of between $22m and $28m. Will the painting, which was sold 18 months ago at Sotheby’s for only $17.5m, set a new record for the German artist? It may be difficult to tell.

Like 38 other works in the Christie’s postwar and contemporary sale, “Abstraktes Bild (712)” has a guaranteed bid, which means it is bound to sell. Like five others, the undisclosed minimum bid has been promised by an anonymous collector or dealer who may also participate in the auction. A byzantine fee structure means that if he or she wins, the Richter’s true price will be less than the headline suggests.

In the notoriously tricky and opaque art market, where dealers do their best to avoid either displaying prices or disclosing to anyone (often including the artist) exactly what a work is worth, public auctions are the last redoubt of open pricing. Now, as Christie’s and Sotheby’s compete fiercely for business, it is losing ground there.

The shift towards auction houses acting more like private dealers and less like public markets received an additional push this week when Dan Loeb, the hedge fund activist and art collector, largely won his battle with Sotheby’s over what he regards as its old-fashioned ways. Mr Loeb will join its board with two others nominated by his Third Point fund.

Mr Loeb, who described Sotheby’s as “an old master painting in desperate need of restoration”, wants it to stop discounting commissions so heavily and “use its capital more aggressively, sometimes jointly with trusted partners, to secure works for private sale and auction”. Those “trusted partners” tend to be art dealers and hedge fund collectors rather similar to him.

In one sense, shenanigans in the upper echelons of the art market – especially in the contemporary art world, where intrinsic value and price bear very little relationship to each other – do not matter terribly. As in the VIP baccarat room at a Macau casino, if you cannot afford to lose millions by gambling, you should not be playing alongside the high-rollers who can.

But Christie’s and Sotheby’s have more than their own reputations to consider. Art auction houses bring together buyers and sellers in what is at least an approximation of a public market (allowing for tricks of the trade such as “chandelier bids” made up by auctioneers to meet the reserve). Without some transparency at such auctions, the entire market is vulnerable to fraud.

Since the price-fixing scandal of the 1990s, Christie’s and Sotheby’s have battled for the right to sell the most valuable works, and guarantees are one way to gain an advantage. “The auction houses are effectively a duopoly and will do almost anything to maintain that,” says Jeff Rabin, cofounder and principal of Artvest, a New York advisory firm.

They often waive the standard 10 per cent seller’s fee to auction a prestigious work, and offer the seller a share of the 12.5 per cent paid on top of the purchase price by the buyer. Some sellers also demand a guarantee – a promise that the auction house will buy the work if it does not meet its reserve, saving them the embarrassment.

But these guarantees involve risk, as Sotheby’s was reminded in 2008, when it was left with $50m of works it guaranteed before the financial crisis. The art market’s chronic lack of transparency and the ever-present suspicion that dealers are artificially inflating prices means any painting that does not sell is instantly discounted by a third.

Christie’s and Sotheby’s now pass off risk on some of the most valuable works to dealers or collectors. The latter put up their capital in return for a fee, and a share of takings of a strong auction. Sotheby’s disclosed in April that it had made $279m of guarantees, of which $65m had been laid off to third parties, and the latter figure has since risen.

A sophisticated collector can get a good return from being a guarantor, particularly at Christie’s. If he, for example, owns several Richters, and wants the prices to stay buoyant, he can not only support the market but also be paid for doing so. The worst case is having to pay the guaranteed bid, less fee, for another Richter.

If the guarantor loses the auction to a rival bidder, he gets both the fee and a slice of the proceeds above the price he guaranteed. If he wins, he can, in effect, end up paying less than the published price since Christie’s allows him to offset the guarantee fee against the winning bid.

Giving a guarantor such privileges distorts the auction by allowing one bidder to participate on better terms than others. It also makes the result hard to understand, or derive price information from. The only clue to a third-party guarantee is a tiny diamond symbol (Christie’s) or backward C (Sotheby’s) inscribed in the auction catalogue by a work. The outsider is not told if a guarantor is also bidding, or whether the insider later wins the auction.

Sotheby’s does not allow guarantors who win auctions the same attractive terms. But its share of contemporary art auctions, for which many guarantees are offered, is five points below its overall share of 47 per cent, and the pressure is intense. “The old loyalties have gone. Sellers now select the house that offers them the best deal,” says Anders Petterson, managing director of ArtTactic, an advisory firm.

A first test for Sotheby’s, with Mr Loeb now on its board, is whether it will stick to its principles or venture further into opaque deals and private guarantees. The rest of the market has plenty to lose.